A Request and a Psych Analysis Puzzle

You won a free ticket to see an Eric Clapton concert (which has no resale value). Bob Dylan is performing on the same night and is your next-best alternative activity. Tickets to see Dylan cost $40. On any given day, you would be willing to pay up to $50 to see Dylan. Assume there are no other costs of seeing either performer. Based on this information, what is the opportunity cost of seeing Eric Clapton? (a) $0, (b) $10, (c) $40, or (d) $50.

First the request :

Please suggest a phrase that can be used to substitute for 'net benefit' if the advantages and disadvantages do not share a common unit and therefore, cannot be involved in a subtraction.

Then the puzzle:

What possible rationale might help to explain why my answer to the problem above, if restricted to dollars, would be $22.50?

The entire point to the opportunity cost concept is that one is comparing two events, either the two most preferred (from a utility standpoint) or the only two available. As such, one is set as a baseline, so your comment about advantages and disadvantages not sharing the same scale is not applicable. For convenience, in this problem, they slid the scale and put Clapton at Zero. Also, the "net benefit" is not a true benefit since only one action can take place. Instead, it is in regards to the expected difference in utility absorbed through the actions.

The entire framework rests on the notion of indifference, which allows us to compare two hypothetical states. For your opportunity cost to be $22.50 implies that you are indifferent to the two situations
Dylan - $40 - $22.50 and Clapton
Which also implies
Dylan - $40 and Clapton + $22.50
Which also implies that on this day, you would be willing to pay up to $62.50 for Dylan which violates the assumptions.

If you want to relax the restriction to place Clapton at Zero, then it is possible that on any given day you would pay $50 to go see Dylan and someone would therefore have to pay you to go see Clapton, but that implies a third option - doing nothing - which is now placed at zero (and is now the second best option), which puts you right back where you were at $10.

The 'Net Benefit' that I'm looking for a substitute for is the one that refers to the Dylan concert all by itself. The advantage is the subjective appreciation of the musical performance and the disadvantage is paying some number of dollars for a ticket. Calling this combination of advantages and disadvantages a 'net benefit' implies that the disadvantages can be subtracted from the advantages, which is not possible.

As for the request, how about change "net benefit" to "surplus subjective value"?

From the defintions of opportunity costs that I've read (granted I'm no professional economist), I can't see how you could come up with an opportunity cost of the Dylan show other than $50 (your gross subjective value of the show) or $10 (your net subjective gain from going to the show).

If I go to see Clapton, I have the experience of seeing Clapton + $40. If I forego seeing Dylan, I miss out on the experience of seeing Dylan - $40. My opportunity cost isn't $10, but $10 of bonus Dylan entertainment. This is a subtle, but important distinction and supports your desire for a term to replace "net benefit" that more accurately describes what is really being gained or lost.

But I'm not sure if breaking down opportunity cost into a "net benefit" is how people actually make decisions. Say I value Clapton at $12.50. I won a free ticket, I should go to his show. But if I value Dylan at $50... that means I like Dylan 4x as much. If I've got the $40 bucks on me, I'm going to see Dylan! Yeah! All along the Watchtower! Rock on! Now if I sat down and computed the opportunity cost, I would see that I should actually go see Clapton because:
the enjoyment of his show plus forty dollars
is $2.50 of my subjective enjoyment value greater than
a Dylan show - $40.

Bottom line, I guess, is that I think opportunity cost attempts to put a concrete figure to a subjective concept in a way normal people don't always relate to.

As for the request, how about change “net benefit” to “surplus subjective value"?

A good try, but it doesn't say to me quite what I want and only what I want.

My best current substitute is 'aggregate benefit', but I'm not really happy with it either.

From the defintions of opportunity costs that I’ve read (granted I’m no professional economist), I can’t see how you could come up with an opportunity cost of the Dylan show other than $50 (your gross subjective value of the show) or $10 (your net subjective gain from going to the show).

As a reward for your willingness to address both parts, I will give you a hint that will likely really convince you that I need professional help.

Starting with the given willingness to pay up to $50, and the $40 ticket price, I would agree that the dollar answer would be $10 if the following were true, as an example :

I expect to arrive at the Dylan concert and find that, instead of giving a performance, they hand out $50 worth of gold, euros, or stock certificates.

You're mixing subjective and objective, and are in danger of (re)staring a VERY long series of posts that don't really go anywhere :)

Andy's comment that the entire framework rests on the notion of indifference is absolutely key here. The term you're looking for is, in fact "net benefit", but you're trying to measure in utils, the subjective measure of utility, which may or may not exist in any meaningful sense,and may or may not be comparable to itself, let alone other measures.

Don't do that.

Instead, make the simplifying assumption (which is incorrect in many cases, but close enough sometimes to work, kinda) that there is a currency value for any preference you have, measurable by the amount at which you're indifferent to the money or the event. Call this amount the net benefit, and such calculations become easy.

I really don't see how you can get 22.50. If you choose to go to the Clapton concert, it means you forego seeing the dylan concert and losing $40. You value the dylan concert at $50, and you value $40 at $40, so the total opportunity cost is $50 - $40, or $10.

You’re mixing subjective and objective, and are in danger of (re)staring a VERY long series of posts that don’t really go anywhere

This isn't quite the particular swamp that I'm headed for, and I'm hopeful that its protective barriers are functional.

Andy’s comment that the entire framework rests on the notion of indifference is absolutely key here. The term you’re looking for is, in fact “net benefit", but you’re trying to measure in utils, the subjective measure of utility, which may or may not exist in any meaningful sense,and may or may not be comparable to itself, let alone other measures.

No, I won't allow utils in the same town, let alone the house.

My concern is having a combination of entertainment (etc.) benefit and money prices. I want to be able to refer to this combination without or at least before converting to dollars.

I really don’t see how you can get 22.50. If you choose to go to the Clapton concert, it means you forego seeing the dylan concert and losing $40. You value the dylan concert at $50, and you value $40 at $40, so the total opportunity cost is $50 - $40, or $10.

"Starting with the given willingness to pay up to $50, and the $40 ticket price, I would agree that the dollar answer would be $10 if the following were true, as an example :

I expect to arrive at the Dylan concert and find that, instead of giving a performance, they hand out $50 worth of gold, euros, or stock certificates."

Don, considering how meticulous you are being, I would expect you to mention that there are liquidity and transaction costs to being paid in something other than dollars in these United States (Or perhaps there is a premium associated with owning gold). Hence 50 dollars in dollar bills and 50 dollars worth of Euros or gold could not be apriori valued as the same as 50 dollars...

Don, considering how meticulous you are being, I would expect you to mention that there are liquidity and transaction costs to being paid in something other than dollars in these United States (Or perhaps there is a premium associated with owning gold). Hence 50 dollars in dollar bills and 50 dollars worth of Euros or gold could not be apriori valued as the same as 50 dollars…

For present purposes, nominal values are fine. Otherwise, what you say is true.

In response to: You value the dylan concert at $50, you said this is an invalid conclusion.

I say this is not a conclusion, but a premise. The problem states there are no other costs to seeing either performer, and that your value for a dylan constant is fixed (well, "on any given day", at least). And the definition of indifference curve, without which opportunity cost is meaningless, includes consistency and transitivity.

If you claim that you value a dylan concert at other than $50, you've violated the terms of the puzzle. Or you've rejected consistency in indifference curves, and must therefore reject the puzzle's question. This is IMO a valid rejection, as it's clear that people are often not consistent, but it breaks the model of valuation which includes opportunity cost.

I suspect it's this consistency which is troubling you. You are willing to spend up to $50 for a dylan ticket, but you would not sell your dylan ticket for $51. Without that consistency, you can't make numerical comparisons based on unlike commodities.

I suspect it’s this consistency which is troubling you. You are willing to spend up to $50 for a dylan ticket, but you would not sell your dylan ticket for $51. Without that consistency, you can’t make numerical comparisons based on unlike commodities.

Just the opposite, this belief in consistency is the fundamental error of Behavioral Economics. But we're not worried about resale here.

Given 'spend up to $50', is the conclusion 'value at $50' universally correct, or even rational?

I thought about this question for a while when it first appeared on MR until I realized that I don't know and I don't care and the fact that economists think this is such a fascinating brain-teaser is Factoid #1,210,212 that there's something deeply pathological about the dismal science.

"Given ’spend up to $50?, is the conclusion ‘value at $50? universally correct, or even rational?"

And the answer is: yes. Yes it is (rational, at least). All the question is doing is setting up your consumer surplus over market price. You have to forego that consumer surplus to go see Clapton. The more times you revisit this topic, the more confused I become with your question. What is it that I am missing about your objection? It seems to me that you are taking a very simple question and attempting to make it more complicated for reasons that are unnecessary given the purpose of the question.

And the answer is: yes. Yes it is (rational, at least). All the question is doing is setting up your consumer surplus over market price. You have to forego that consumer surplus to go see Clapton. The more times you revisit this topic, the more confused I become with your question. What is it that I am missing about your objection? It seems to me that you are taking a very simple question and attempting to make it more complicated for reasons that are unnecessary given the purpose of the question.

Your hint:

Is money scarce?

Regards, Don

PS I'm temporarily refraining from explaining myself fully in order to allow the possibility of someone working it out in a similar or related way, to our mutual benefit.

Your willingness to pay $50 for a Dylan concert does NOT mean a Dylan concert has a perceived utility of $50, since the opportunity cost of attending the Dylan concert is at least $50 plus the benefit of the best free thing you could have done that night with the available time. More accurately, it is the best of all possible alternatives that night when considering the value of the activity and the cash price. That's why you would have been royally ticked off if you paid $50 for the concert and, when you showed up, were simply handed $50 (essentially nothing but a refund after foregoing the pleasure of browsing the Internet all night instead of driving to the Dylan concert and returning home). The tricky part is figuring out what you could have gotten for $50 AND your time that day, but it is clear that the highest pleasures (or income) you could have obtained during the time spent traveling to the Dylan concert, being there, and traveling home must be worth more than zero to you, so the gross value of the Dylan concert must be substantially higher than $50 to you, and the opportunity cost of choosing something else MUST be substantially higher than $10. Thus, we can reject $10 as the correct answer.

Okay, deep breath ... how the heck did you come up with $22.50 ... hmmm ... well, if the availability of Dylan tickets that you would have been willing to pay $50 to receive are selling for $40, that suggests that the equilibrium of prices is such as to make available a 25% return on spending. Your willingness to pay $50 suggests that, if your return on investment is in equilibium, that you perceive a value of the Dylan concert at 25% above $50, or $62.50. Since you would have to pay $40 to attend that concert, the net benefit from attending the Dylan concert is $62.50 - $40.00 = $22.50, and if you attend the Clapton concert, that is your opportunity cost.

After giving it a great deal of thought, my suggested alternative term for "net benefit" is "2 aspirin and a glass of water."

Okay, deep breath … how the heck did you come up with $22.50 … hmmm … well, if the availability of Dylan tickets that you would have been willing to pay $50 to receive are selling for $40, that suggests that the equilibrium of prices is such as to make available a 25% return on spending. Your willingness to pay $50 suggests that, if your return on investment is in equilibium, that you perceive a value of the Dylan concert at 25% above $50, or $62.50. Since you would have to pay $40 to attend that concert, the net benefit from attending the Dylan concert is $62.50 - $40.00 = $22.50, and if you attend the Clapton concert, that is your opportunity cost.

Very good, except that I didn't take time into consideration.

If you added up all the money you spent in supermarkets over the last year, what benefit did you get for it?

Notwithstanding my opening quote, I don't think I directly considered time in my calculations: I was simply referring to the fact that the alternative to spending money on the Dylan concert was not simply doing nothing that day, so that any calculation of the cost of attending the Dylan concert must consider the alternative pleasurable activities that could have taken up that time period. That is the reason I would expect some return on spending, and would never pay $50 for the Dylan ticket if the value of the concert to me was only $50. But without alternatives, my choice is costless. Indeed, if the only thing I could do with my money is buy a Dylan ticket, they might as well charge my entire net worth, since the money is otherwise useless to me. It wouldn't change the value of the concert to me, but would change what I was willing to pay.

Of course, we could just limit the discussion to the different things I could have done with $50, and pretend the benefits are instant (just what I wanted: to pay $50 for a 1 second Dylan concert!). It doesn't change the fact that the price I'm willing to pay is going to be much lower than the value I expect to receive, as long as I have other alternatives with positive net benefits. And the implied 25% return being the point on the indifference curve still remains my only way of deriving your numbers (when I first saw the MR multiple choice question, I instantly answered $10, as they thought I should, because they learned me good in college).

Sorry, but I have no idea where you're headed with the supermarket question. I can give trite answers about the benefits I receive (food, survival, pleasurable sensations on the tongue and in the belly, waste products), but no obvious quantitative answer occurs to me. Except 730 aspirin, at the rate I'm going.

For any given consumer good, for any given consumer, at a given time, there is always some hypothetical price that, if paid, would completely and exactly offset the benefit that the good itself could be expected to provide.

I want to be a little careful in my answer. I don't believe this is always true - I tend to think people are less consistent and rational than is implied by the normal description of an indifference curve, and I think values are less often transitive than is normally assumed.

I do, however, believe that this is a tenet of the economic model in which "opportunity cost" is used and defined, and that such a model is useful for many predictions.

For any given consumer good, for any given consumer, at a given time, there is always some hypothetical price that, if paid, would completely and exactly offset the benefit that the good itself could be expected to provide.

Specifically, the marginal expected benefit of the money is exactly equivalent to the marginal expected benefit of the other good. The consumer is truly indifferent between them. This benefit can be denominated in dollars because the values are identical.

Given the above, and leaving the evaluation of the consequences for later, the consumer has the ability to
set and follow a rule that specifies what maximum percentage of the benefit-offsetting price above he is willing to pay.

Your rule would say 100% and my rule would say 80%.

Here I disagree. Given the above, the rule can only be that everyone is willing to spend up to 100% of the value of the good, or they are lieing about the value of either the good or the money. In fact, it's not a rule that can be chosen, it's part of the definition. If you're not willing to trade a specific $50 bill for a specific concert, then that concert does not have more value to you than the note.

Values are equal only at the limit of a trade that an individual would make. If you wouldn't make the trade, the values aren't equal.

Of course, we could just limit the discussion to the different things I could have done with $50, and pretend the benefits are instant (just what I wanted: to pay $50 for a 1 second Dylan concert!).It doesn’t change the fact that the price I’m willing to pay is going to be much lower than the value I expect to receive, as long as I have other alternatives with positive net benefits. And the implied 25% return being the point on the indifference curve still remains my only way of deriving your numbers (when I first saw the MR multiple choice question, I instantly answered $10, as they thought I should, because they learned me good in college).

If I could tell you that you would have to be awfully rich to run out of things to buy whose benefits are worth at least 25% more to you than their price before you run out of the money to buy them, would that have implications about your willingness-to-pay?

If you run out of such things to buy today, won't more come along tommorrow if you don't spend all your money today?

You definitely have points worth consideration that I can't immediately pass a judgment on.

The willingness to pay up to $50 must take into account that you have immediate or future alternate uses of this specific marginal $50. We’ve been told that you would prefer the dylan concert and losing $50 to the best next alternate (no concert and keeping your $50) on “any given day", so we know that within the confines of the problem, there is no uncertainty nor variance in the value of a dylan concert compared to $50.

Let's see if we can find a point of agreement before any divergence occurs.

Do you agree with the following statement? --

For any given consumer good, for any given consumer, at a given time, there is always some hypothetical price that, if paid, would completely and exactly offset the benefit that the good itself could be expected to provide.

Given the above, and leaving the evaluation of the consequences for later, the consumer has the ability to
set and follow a rule that specifies what maximum percentage of the benefit-offsetting price above he is willing to pay.

Your rule would say 100% and my rule would say 80%.

Which is more beneficial, given a limited amount of money to spend, is probably determined by the overall supply and price array of consumer goods.

My rule denies me the benefits of any goods that are priced above 80% of the benefit-offsetting price.

Your rule uses up money on the goods of relatively low 'net' benefit that I have denied myself.

If I could tell you that you would have to be awfully rich to run out of things to buy whose benefits are worth at least 25% more to you than their price before you run out of the money to buy them, would that have implications about your willingness-to-pay?

It would have implications about the depth of the divide we have between our understanding of this model of value. I claim you (and I, and everyone) HAVE run out of things that are valued more than any alternate (taking into account all costs, not just dollars). Otherwise, you'd make the best trade available until you have no more good deals available. If you have better deals expected tomorrow than you have available today, that just means your dollars are worth more than today's available good, and you should keep them.

The willingness to pay up to $50 must take into account that you have immediate or future alternate uses of this specific marginal $50. We've been told that you would prefer the dylan concert and losing $50 to the best next alternate (no concert and keeping your $50) on "any given day", so we know that within the confines of the problem, there is no uncertainty nor variance in the value of a dylan concert compared to $50.

If you run out of such things to buy today, won’t more come along tommorrow if you don’t spend all your money today?

Sure, but that's part of the definition of indifference between the $50 and a dylan concert.

A ten dollar bill and a twenty dollar bill are lying on the ground. God comes down from the heavens and says that you can take one and only one of these bills. If you choose the twenty, what is the opportunity cost you incurred?

The answer is $10. And this is basically the same problem that's being discussed, where Dylan is the ten and Clapton is the twenty.

It costs $40 to see Dylan, and you value him at $50, so the net benefit to you of seeing Dylan is $10. He's like a ten spot chillin' on the sidewalk.

If you choose to see Clapton instead of Dylan, then the net benefit you get from the former must exceed the latter. Since Clapton costs $0, you must value him at $10 or more --- in that sense, he's like a twenty catchin' rays on the blacktop.

If you choose Clapton over Dylan, you choose a free twenty over a free ten. So the opportunity cost in this situation is $10. I have no idea what all the hubbub is about.

Looking at it from a more refined version of my initial angle, the bills on the pavement are a fifty and a twenty, and God will charge you ten bucks to get at the twenty. If you choose the fifty, the conclusion is the same --- the opportunity cost is $10. This is because it will cost you $10 to get the twenty, so you'll only derive $10 in benefit from it.

All of this complication seems to result from deviating from the principle of revealed preference. I might actually value Dylan at more than $50, but if I'm only willing to spend $50 to see him, then for all anybody can practically know (myself included), he's worth $50 to me. If you can deduce new truths by ditching revealed preference, let me know. Otherwise, I'm sticking with the boring answer: $10.

1. You are not seeking the best condition, which is the most basic assumption of economics, that man seeks to improve his condition.

or

2. There is something you are not accounting for in your valuation. It is important to think of decisions in terms of future states rather than outcomes. You are making a decision based on your expected future state of the world which encompasses far more than just what concert you go to. Your 80% rule probably implies that you at any given time expect to have higher "net benefits" from future options, as well as low liquidity and low credit-worthiness since you fear not being able to take advantange of those options. The problem with such a heuristic is that utilizing a percentage like this would lead to some poor decisions when dealing with a high payoff event.

Here I disagree. Given the above, the rule can only be that everyone is willing to spend up to 100% of the value of the good, or they are lieing about the value of either the good or the money. In fact, it’s not a rule that can be chosen, it’s part of the definition. If you’re not willing to trade a specific $50 bill for a specific concert, then that concert does not have more value to you than the note.

I read the above as saying that every trade offered that has a non-negative (or possibly positive) benefit must be taken.

If you have finite money, the risk is that you can't predict the time order of trades offered and that you may exhaust your money on early, low benefit trades.

I read the above as saying that every trade offered that has a non-negative (or possibly positive) benefit must be taken.

"must" in the definitional sense (like "if you write down an even number, it must be a multiple of 2"). It's not that you decide on values, then choose to trade, it's that you decide whether to trade, and that is the definition of value.

If you have finite money, the risk is that you can’t predict the time order of trades offered and that you may exhaust your money on early, low benefit trades.

Sure - it happens all the time. You later find that you've taken an action that you wouldn't make now. Valuations change with different circumstances.

Alternatively, if you anticipate finding something you value more, that just adds to the value of the "no trade" option, possibly making it more valuable than the trade. In which case you won't trade.

The definition remains: if you won't make a trade, you value the no-trade situation more than the trade situation. If you will trade, you value the trade more. That's it. That's all there is.

If you buy the dylan ticket, and tomorrow learn of a concert you think you'd rather see but can no longer afford, that's a change in situation. If you forego the dylan ticket because you think there's a better concert tomorrow, you are simply valuing the $50 more than the dylan ticket, even if you turn out to be wrong and tomorrow's concert is cancelled.

"For any given consumer good, for any given consumer, at a given time, there is always some hypothetical price that, if paid, would completely and exactly offset the benefit that the good itself could be expected to provide." -- me

I want to be a little careful in my answer. I don’t believe this is always true - I tend to think people are less consistent and rational than is implied by the normal description of an indifference curve, and I think values are less often transitive than is normally assumed. -- you

For this, we don't need an indifference curve, but only an indifference point. (agree?)

Specifically, the marginal expected benefit of the money is exactly equivalent to the marginal expected benefit of the other good. The consumer is truly indifferent between them. This benefit can be denominated in dollars because the values are identical. -- you

I want to rephrase this because only the good side is a benefit. I prefer that we say that the consumer is indifferent between the original comprehensive state and an expected modified state that would result from the idealized effects of a proposed exchange.

In determining the hypothetical benefit-offsetting price, there is no actual transaction and no transaction costs.

In addition, there is nothing in this procedure that says the price needs to be in dollars or money. The terms of a ticket could equally well specify cookies or the destruction of a number of your nuclear weapons.

What is important is that we end up with indifferent states.

Be that as it may, if you say that you would be willing to pay up to 100% of the benefit-offsetting price, that doesn't say that any such exchange has ever or will ever necessarily take place. This would also be true if your limit was 99% or 95%. The lower the residual benefit, and the higher the supply and variation of consumer goods, the higher the probability that it will be merely the opportunity cost of a preferred substitute.

The entire free market inherently tends to drive product prices down to allow even people with low expected benefits for the product to benefit from buying them.

The key is the wide variation in the perceived benefits of consumer products. If all consumers were identical clones, prices would be higher, and the 'net' benefits would be lower.

You cannot have an “indifference point". The whole idea of an indifference curve is that it is a set of points describing various bundles of goods to which one is indifferent. If you only have one point, to what are you indifferent?

Good point. An "indifference pair", or a collection of them into an "indifference table", is what I should have said. I certainly don't need a continuous, differentiable "indifference curve".

In short, I continue to believe that you are taking a really simple and reasonably clear question and making it infinitely more complicated than you need to, for reasons that are totally unclear to me.

You may well be right, but how can I know how complicated I need to make a question in advance?

Maybe you are willing to pay up to 100% of the expected dollar benefit of a consumer good, but neither the empirical evidence nor an audit of your past purchases is likely to provide much, if any, support for that.

If we were to investigate the register tape of your last trip to the supermarket, and, separately, item by item, assign a higher price which would have just prevented that item from appearing in your shopping cart, what would the range of percentage increases in prices be?

If you paid $3/gal for 10 gallons of gas on your last trip to the gas station, what price/gal. and percentage increase would have reduced your purchase to 5 gallons?

I know that this argument has no validity for the question, but it is interesting just how much dollar benefit premium an average dollar spent actually buys for consumer goods.

You cannot have an "indifference point". The whole idea of an indifference curve is that it is a set of points describing various bundles of goods to which one is indifferent. If you only have one point, to what are you indifferent?

I get your point (I think): the $10 answer doesn't take into account the possibility of even better trades tomorrow. The short answer is "so what?" The point of the question is frame it such that the tradeoff is between exactly two concerts. That's it. Not more. Not less.

In short, I continue to believe that you are taking a really simple and reasonably clear question and making it infinitely more complicated than you need to, for reasons that are totally unclear to me.

To all of your points (on consumer surplus over price): sure, it is interesting. But what are you trying to get at? I'm genuinely confused at your objection?... confusion?... reformulation?... of the opportunity cost question.